Two-atom quantum gate in hybrid cavity optomechanics

Tracing the dynamics of a quantum system using a mesoscopic device is an important topic of interest nowadays. Here we show how a mesoscopic mechanical oscillator steers the dynamics of a coupled two-atom system and gives rise to a two-qubit SWAP gate. We have theoretically studied a generic hybrid atom-optomechanical system where two identical atoms in $\mathrm{\Lambda }$ configuration are trapped inside the cavity and the cavity mode mediates the interaction between the atoms and the mechanical oscillator. Adiabatic elimination of the lossy channels is adopted which in turn gives rise to an effective Hamiltonian that is responsible for a two-atom SWAP gate controlled by the mechanical motion of the oscillator. The validity of the proposal for successful implementation is assessed using presently available experimental parameters.